Import context: KLS/LogConcave/Density/GaussianSmoothing/Moments

Definition

KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_Moments

by Lazyfill · Oct 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

functional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-context

This bundle retains the import context of the source module FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Moments in the modular KLS dependency graph. It adds no new mathematical declarations. Substantive statements and proofs are represented by separate theorem nodes.

Its direct project prerequisite modules are FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Basic, FunctionalInequalities.Analysis.BakryEmery.Tilt.LocalDerivatives, FunctionalInequalities.Probability.Product, FunctionalInequalities.Probability.Covariance.Basic, FunctionalInequalities.Analysis.WeakDerivative.Basic, FunctionalInequalities.Analysis.WeakDerivative.Calculus, and FunctionalInequalities.KLS.LogConcave.Density.BorellRepresentation.Moments. It also directly imports the external prerequisite module Mathlib.MeasureTheory.Group.IntegralConvolution.

Original module imports

import FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Basic
import FunctionalInequalities.Analysis.BakryEmery.Tilt.LocalDerivatives
import FunctionalInequalities.Probability.Product
import FunctionalInequalities.Probability.Covariance.Basic
import Mathlib.MeasureTheory.Group.IntegralConvolution
import FunctionalInequalities.Analysis.WeakDerivative.Basic
import FunctionalInequalities.Analysis.WeakDerivative.Calculus
import FunctionalInequalities.KLS.LogConcave.Density.BorellRepresentation.Moments

Module navigation

Direct project imports: KLS/LogConcave/Density/GaussianSmoothing/Basic, Analysis/BakryEmery/Tilt/LocalDerivatives, Probability/Product, Probability/Covariance/Basic, Analysis/WeakDerivative/Basic, Analysis/WeakDerivative/Calculus, KLS/LogConcave/Density/BorellRepresentation/Moments.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Moments · Frozen source 408915f.

Definition code

import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_BakryEmery_Tilt_LocalDerivatives
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Product
import Definitions.Def_KLSModular_FunctionalInequalities_Probability_Covariance_Basic
import Mathlib.MeasureTheory.Group.IntegralConvolution
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_WeakDerivative_Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_WeakDerivative_Calculus
import Definitions.Def_KLSModular_FunctionalInequalities_KLS_LogConcave_Density_BorellRepresentation_Moments

Source

Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/KLS/LogConcave/Density/GaussianSmoothing/Moments.lean#L1-L569 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.KLS.LogConcave.Density.GaussianSmoothing.Moments`, import-context bundle `KLSModular_FunctionalInequalities_KLS_LogConcave_Density_GaussianSmoothing_Moments`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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